Firstly, it is known that at large \(Z\)  the ground state energy can be estimated by the \(1/Z\)  perturbative expansion [1]},
\(E(Z)\ =\ -B_0\, Z^2 \ + \ B_1\, Z\ + \ B_2 \ + \ O\bigg (\frac{1}{Z}\bigg )\ ,\) 
